SHANGHAI, Nov 2 (Reuters) - China's central bank tightened its grip on yuan appreciation with a second straight weaker midpoint fixing on Friday, pushing the yuan slightly lower, but traders said demand for the currency remained robust.

The central bank fixed the yuan's midpoint at 6.3045 per dollar, down from Thursday's 6.3017 and the weakest level in a week. The People's Bank of China has kept the midpoint virtually flat since Oct. 17.

That suggests the central bank may have lost its appetite for further yuan strengthening and that the recent period of steep appreciation may be over, said traders.

``Overall, I see the yuan continuing to rise but in the short term we may well see a bounce against the dollar,'' said a trader at a city commercial bank in Shanghai.

Traders said that central bank guidance in the form of weaker fixes and informal influence on state-owned banks had slowed the yuan's rise since mid-October.

The central bank had previously set a string of sharply stronger fixes, between Oct. 11 and Oct. 17, which allowed the yuan to appreciate strongly against the dollar to a record strong close of 6.2372 earlier this week.

The yuan opened on Friday at 6.2432 per dollar, weaker than Thursday's close of 6.2405, before strengthening slightly to 6.2428 around midday.

The weaker fix meant that even if the currency were to hit the day's strong-side limit, it would still fall short of Thursday's weakest level.

Though the yuan/dollar rate never looked likely to trouble the strong-side barrier, traders said that demand remained strong as banks continued to unwind long dollar positions built up during the U.S. currency's rise at the start of the year.

That kept the rate close to the strong-side limit, and meant that in morning trading the high/low trading range posted its narrowest divergence since March.

The exchange rate can rise or fall 1 percent from the mid-point set by the central bank each day.

Some analysts agreed that the central bank may have sated its appetite for yuan appreciation, and that the currency may now flatten, or weaken slightly, against the dollar in the coming months.

The dollar index rose overnight, maintaining its bounce since hitting a week low on Oct. 31. The yuan traditionally tracks the euro and other global currencies against the dollar.